Two-Part Models for Analysis of Agatston Scores with Possible Proportionality Constraints

Abstract

ABSTRACT Logit-linear and probit-linear two-part models can be used to analyze data that are a mixture of zeros and positive continuous responses. The slopes in the linear part of a model can be constrained to be proportional to the slopes in the logit or probit part. In this article, it is shown that implementing such a constraint will decrease (in Loewner ordering) the asymptotic covariance matrix of the maximum likelihood estimates. A case study is provided using coronary artery calcification data from the Multi-Ethnic Study of Atherosclerosis.